IMPORTANT: (nth root of k)^n = kvinay1983 wrote:What is the value of X, given X is a positive number?
1. X^3 is a 2 digit positive odd integer
2. X^4 is a 2 digit odd integer.
Examples: (square root of 9)^2 = 9
(square root of 22)^2 = 22
(cube root of 64)^3 = 64
(fourth root of 19)^2 = 19
Okay, onto the question. . . .
Target question: What is the value of X?
Given: X > 0
Statement 1: X^3 is a 2 digit positive odd integer
There are many values of X that meet this condition. Here are two:
Case a: X = 3, since 3^3 = 27, a 2-digit number.
Case b: X = cuberoot of 11, since (cuberoot of 11)^3 = 11, a 2-digit number.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: X^4 is a 2 digit odd integer.
There are many values of X that meet this condition. Here are two:
Case a: X = 3, since 3^4 = 81, a 2-digit number.
Case b: X = fourth root of 11, since ( fourth root of 11)^3 = 11, a 2-digit number.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
From both statements combined, we can conclude that X is an integer. Here's why?
We know this because X^3 and X^4 are both integers.
Notice that X^4 = (X^3)(X)
Let's assume for a moment that X is a non-integer. If X^3 is an integer, and X is a non-integer, then their product (X^4) cannot be an integer. So, X must be an integer.
If X is an integer, X must equal 3, since this is the only integer that yields 2-digit numbers when cubed and raised to the fourth power.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
). 
